Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The usefulness of node2vec in these applications is considered to be contingent upon properties of random walks that the node2vec algorithm uses. In the present study, we theoretically and numerically analyze random walks used by the node2vec. The node2vec random walk is a second-order Markov chain. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyze the stationary probability, relaxation times, and coalescence time. In particular, we provide a multitude of evidence that node2vec random walk accelerates diffusion when its parameters are tuned such that walkers avoid both back-tracking and visiting a neighbor of the previously visited node, but not excessively.
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